a) Use loopshaping to design a controller that achieves a loop bandwidth of L = 5 rad/sec. Your design should have a phase margin 45 . (b) Use loopshaping to design a controller that achieves a higher (faster) loop bandwidth of L = 50 rad/sec. Your design should have a phase margin 45 . (c) Create a Bode plot with both of the loops L1(s) = G(s)K1(s) and L2(s) = G(s)K2(2). (d) Generate a closed-loop step response with a unit reference commands for both designs. Create two separate plots: (i) a plot showing the output y vs. time t for both designs for t [0, 1.5] sec, and (ii) a plot showing the control u vs. time t for both designs for t [0, 1.5] sec. Comment on the speed of response and control effort required by the two designs both during the initial transient and in the steady-state. [Hint: How is the steady-state control signal u related to the plant DC gain